Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsGeneral (Definition,type and special type)Easy2 minQB

MathematicsEasyinteger

If $f (x + y, x - y) = x y$ , then the arithmetic mean of $f (x, y)$ and $f (y, - x)$ is $____$

Answer:

Solution:

$x + y = a, x - y = b \Rightarrow x = \frac{a + b}{2}, y = \frac{a - b}{2}$

$f (a, b) = (\frac{a + b}{2}) (\frac{a - b}{2}) = \frac{a ^{2} - b ^{2}}{2}$

$A \cdot M = \frac{f ( x \cdot y ) + f ( y , - x )}{2} = \frac{x ^{2} - y ^{2} + y ^{2} - x ^{2}}{4} = 0$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:General (Definition,type and special type)

⏱ 2mℹ️ Source: QB

Loading discussions...